Uncertainty principles for locally compact quantum groups

In this paper, we prove the Donoho–Stark uncertainty principle for locally compact quantum groups and characterize the minimizer which are bi-shifts of group-like projections. We also prove the Hirschman–Beckner uncertainty principle for compact quantum groups and discrete quantum groups. Furthermore, we show Hardy's uncertainty principle for locally compact quantum groups in terms of bi-shifts of group-like projections.     

The Applications of Order Reduction Methods in Nonlinear Dynamic Systems

Two different order reduction methods of the deterministic and stochastic systems are discussed in this paper. First, the transient proper orthogonal decomposition (T-POD) method is introduced based on the high-dimensional nonlinear dynamic system. The optimal order reduction conditions of the T-POD method are provided by analyzing the rotor-bearing system with pedestal looseness fault at both ends. The efficiency of the T-POD method is verified via comparing with the results of the original system. Second, the polynomial dimensional decomposition (PDD) method is applied to the 2 DOFs spring system considering the uncertain stiffness to study the amplitude-frequency response. The numerical results obtained by the PDD method agree well with the Monte Carlo simulation (MCS) method. The results of the PDD method can approximate to MCS better with the increasing of the polynomial order. Meanwhile, the Uniform-Legendre polynomials can eliminate perturbation of the PDD method to a certain extent via comparing it with the Gaussian-Hermite polynomials.     

Uncertainty quantification for dynamics of geometrically nonlinear structures coupled with internal acoustic fluids in presence of sloshing and capillarity

In this paper, we propose an uncertainty quantification analysis, which is the continuation of a recent work performed in a deterministic framework. The fluid–structure system under consideration is the one experimentally studied in the sixties by Abramson, Kana, and Lindholm from the Southwest Research Institute under NASA contract. This coupled system is constituted of a linear acoustic liquid contained in an elastic tank that undergoes finite dynamical displacements, inducing geometrical nonlinear effects in the structure. The liquid has a free surface on which sloshing and capillarity effects are taken into account. The problem is expressed in terms of the acoustic pressure field in the fluid, of the displacement field of the elastic structure, and of the normal elevation field of the free surface. The nonlinear reduced-order model constructed in the recent work evoked above is reused for implementing the nonparametric probabilistic approach of uncertainties. The objective of this paper is to present a sensitivity analysis of this coupled fluid–structure system with respect to uncertainties and to use a classical statistical inverse problem for carrying out the experimental identification of the hyperparameter of the stochastic model. The analysis show a significant sensitivity of the displacement of the structure, of the acoustic pressure in the liquid, and of the free-surface elevation to uncertainties in both linear and geometrically nonlinear simulations.     

Analytic hierarchy process for multi-sensor data fusion based on belief function theory

Multi-sensor data fusion is an evolving technology whereby data from multiple sensor inputs are processed and combined. The data derived from multiple sensors can, however, be uncertain, imperfect, and conflicting. The present study is undertaken to help contribute to the continuous search for viable approaches to overcome the problems associated with data conflict and imperfection. Sensor readings, represented by belief functions, have to be fused according to their corresponding weights. Previous studies have often estimated the weights of sensor readings based on a single criterion. Mono-criteria approaches for the assessment of sensor reading weights are, however, often unreliable and inadequate for the reflection of reality. Accordingly, this work opts for the use of a multi-criteria decision aid. A modified Analytical Hierarchy Process (AHP) that incorporates several criteria is proposed to determine the weights of a sensor reading set. The approach relies on the automation of pairwise comparisons to eliminate subjectivity and reduce inconsistency. It assesses the weight of each sensor reading, and fuses the weighed readings obtained using a modified average combination rule. The efficiency of this approach is evaluated in a target recognition context. Several tests, sensitivity analysis, and comparisons with other approaches available in the literature are described.     

Gaussian states as minimum uncertainty states

In bosonic fields, Gaussian states, which consist of a rather wide family of states including coherent states, squeezed states, thermal states, etc., have many classical-like features, and are usually defined from the mathematical perspective in terms of characteristic functions. It is well known that some special Gaussian states, such as coherent states, are minimum uncertainty states for the conventional Heisenberg uncertainty relation involving canonical pair of position and momentum observables. A natural question arises as whether all Gaussian states can be characterized as minimum uncertainty states. In this work, we show that indeed Gaussian states coincide with minimum uncertainty states for an information-theoretic refinement of the conventional uncertainty relation established in Luo (2005) [40]. This characterization puts Gaussian states on a novel basis of physical significance.     

基于不确定控制理论的最优策略研究

本文在不确定理论的框架下,研究一类带背景状态变量的最优控制模型.在乐观值准则下,利用不确定动态规划的方法,证明了不确定最优性原则,得到最优性方程.作为应用,求解一个固定缴费(DC)型养老金的最优投资策略问题,在乐观值准则下,以工资变量为背景状态变量,建立养老金模型.通过求解不确定最优性方程得到最优投资策略和最优支付率.     

Determination of methylmercury in marine sediment samples: Method validation and occurrence data

The determination of methylmercury (MeHg) in sediment samples is a difficult task due to the extremely low MeHg/THg (total mercury) ratio and species interconversion. Here, we present the method validation of a cost-effective fit-for-purpose analytical procedure for the measurement of MeHg in sediments, which is based on aqueous phase ethylation, followed by purge and trap and hyphenated gas chromatography–pyrolysis–atomic fluorescence spectrometry (GC–Py–AFS) separation and detection. Four different extraction techniques, namely acid and alkaline leaching followed by solvent extraction and evaporation, microwave-assisted extraction with 2-mercaptoethanol, and acid leaching, solvent extraction and back extraction into sodium thiosulfate, were examined regarding their potential to selectively extract MeHg from estuarine sediment IAEA-405 certified reference material (CRM). The procedure based on acid leaching with HNO₃/CuSO₄, solvent extraction and back extraction into Na₂S₂O₃ yielded the highest extraction recovery, i.e., 94 ± 3% and offered the possibility to perform the extraction of a large number of samples in a short time, by eliminating the evaporation step. The artifact formation of MeHg was evaluated by high performance liquid chromatography coupled to inductively coupled plasma mass spectrometry (HPLC–ICP–MS), using isotopically enriched Me²⁰¹Hg and ²⁰²Hg and it was found to be nonexistent. A full validation approach in line with ISO 17025 and Eurachem guidelines was followed. With this in mind, blanks, selectivity, working range (1–800 pg), linearity (0.9995), recovery (94–96%), repeatability (3%), intermediate precision (4%), limit of detection (0.45 pg) and limit of quantification (0.85 pg) were systematically assessed with CRM IAEA-405. The uncertainty budget was calculated and the major contribution to the combined uncertainty (16.24%, k = 2) was found to arise from the uncertainty associated with recovery (74.1%). Demonstration of traceability of measurement results is also presented. The validated measurement procedure was applied to the determination of MeHg incurred in sediments from a highly polluted and scarcely studied area in the Caribbean region.     

智能岩石力学及其内容

本文针对岩石力学研究中目前存在的问题和信息时代的要求, 提出了21世纪的智能岩石力学的新思想和研究内容。它是综合现有各种行之有效的方法, 系统研究岩石工程问题, 提高岩石力学解决复杂问题的准确性。     

超导Tl2Ba2CaCu2O8+x 薄膜的太赫兹复电导率的提取

采用低温太赫兹时域光谱系统, 测试了高温超导 Tl2Ba2CaCu2O8+x 薄膜的太赫兹透射谱, 并提取了它在不同温度下的太赫兹电导率. 研究过程中发现提取后的参数存在电导率随频率波动大、与理论值偏差较大等问题.通过对基片厚度和太赫兹波入射角度的误差对高温超导薄膜电导率的影响进行了分析, 结果表明导致数据波动大是由于基片厚度的偏差引起的. 针对厚度差的影响, 一种矫正方法被提出, 通过对厚度的修正, 提高了数据提取的质量.